The college retweeted this "Pop quiz for media" confirming the fact: the college is located in "suburban Lake Worth", not in the City.
You'll find this confirmation on the City's
Wikipedia page:
The main campus of Palm Beach State College is located in unincorporated Lake Worth. It is the oldest community college in Florida, founded in 1933 as Palm Beach Junior College. It was at one time located on the campus of Palm Beach High School, at the present day Dreyfoos School of the Arts in downtown West Palm Beach. The school moved to its present location in 1956. The name was changed to Palm Beach Community College in 1988. In 2010, it was changed to Palm Beach State College to reflect that the school was offering four-year degrees.